Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 27 - Early Quantum Theory and Models of the Atom - General Problems - Page 801: 78

Answer

The fractional mass decrease is $1.29\times10^{-8}$.

Work Step by Step

The emitted photon carries away mass-energy. Calculate the energy of a photon falling from the n = 3 state down to n = 1 state in hydrogen. $$\Delta E=E_3-E_1=-(13.6eV)(\frac{1}{3^2}-\frac{1}{1^2})=12.1eV$$ Calculate the fractional change. $$\frac{\Delta m}{m}=\frac{E_{photon}}{mc^2}=\frac{12.1eV}{939\times10^6eV}=1.29\times10^{-8}$$
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